Department of Engineering, University of Palermo, 90128 Palermo, Italy.
Department of Biomedical Sciences for Health, University of Milan, 20133 Milan, Italy.
Chaos. 2023 Mar;33(3):033127. doi: 10.1063/5.0140641.
This work presents a comparison between different approaches for the model-free estimation of information-theoretic measures of the dynamic coupling between short realizations of random processes. The measures considered are the mutual information rate (MIR) between two random processes X and Y and the terms of its decomposition evidencing either the individual entropy rates of X and Y and their joint entropy rate, or the transfer entropies from X to Y and from Y to X and the instantaneous information shared by X and Y. All measures are estimated through discretization of the random variables forming the processes, performed either via uniform quantization (binning approach) or rank ordering (permutation approach). The binning and permutation approaches are compared on simulations of two coupled non-identical Hènon systems and on three datasets, including short realizations of cardiorespiratory (CR, heart period and respiration flow), cardiovascular (CV, heart period and systolic arterial pressure), and cerebrovascular (CB, mean arterial pressure and cerebral blood flow velocity) measured in different physiological conditions, i.e., spontaneous vs paced breathing or supine vs upright positions. Our results show that, with careful selection of the estimation parameters (i.e., the embedding dimension and the number of quantization levels for the binning approach), meaningful patterns of the MIR and of its components can be achieved in the analyzed systems. On physiological time series, we found that paced breathing at slow breathing rates induces less complex and more coupled CR dynamics, while postural stress leads to unbalancing of CV interactions with prevalent baroreflex coupling and to less complex pressure dynamics with preserved CB interactions. These results are better highlighted by the permutation approach, thanks to its more parsimonious representation of the discretized dynamic patterns, which allows one to explore interactions with longer memory while limiting the curse of dimensionality.
本工作对不同方法进行了比较，这些方法可用于对随机过程短时间实现的动态耦合进行无模型的信息论测度估计。所考虑的测度是两个随机过程 X 和 Y 之间的互信息率 (MIR) 及其分解项，这些分解项可以证明 X 和 Y 的个体熵率及其联合熵率，或者从 X 到 Y 和从 Y 到 X 的转移熵率，以及 X 和 Y 之间共享的瞬时信息。所有测度都是通过对构成过程的随机变量进行离散化来估计的，离散化可以通过均匀量化（分箱方法）或排序（排列方法）来实现。在对两个耦合的非相同 Henon 系统的模拟以及三个数据集（包括心呼吸（CR，心率和呼吸流量）、心血管（CV，心率和收缩压）和脑血管（CB，平均动脉压和脑血流速度）的短时间实现）上，比较了分箱和排列方法。在不同的生理条件下（即自主呼吸与起搏呼吸或仰卧位与直立位），我们的结果表明，通过仔细选择估计参数（即分箱方法的嵌入维度和量化水平数），可以在分析系统中实现有意义的 MIR 及其组成部分的模式。在生理时间序列上，我们发现缓慢呼吸率的起搏呼吸会导致 CR 动态更简单且更耦合，而姿势应激会导致 CV 相互作用失去平衡，与占主导地位的压力反射耦合，同时压力动态变得更简单，但 CB 相互作用保持不变。排列方法更好地突出了这些结果，这要归功于它对离散动态模式的更简洁表示，这使得可以在限制维数诅咒的同时探索具有更长记忆的相互作用。
